System and method for digital-to-analog converter with switched resistor networks

ABSTRACT

A digital-to-analog converter for generating an analog output voltage in response to a digital value comprising a plurality of bits, the converter including: (i) a first switched resistor network having a first configuration and for converting a first input differential signal into a first analog output in response to a first set of bits in the plurality of bits; and (ii) a second switched resistor network, coupled to the first switched resistor network, having a second configuration, differing from the first configuration, and for converting a second input differential signal into a second analog output in response to a second set of bits in the plurality of bits.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.17/537,599 filed Nov. 30, 2021, which is a continuation of U.S. patentapplication Ser. No. 16/950,343, filed on Nov. 17, 2020, now U.S. Pat.No. 11,190,200, which is a continuation of U.S. patent application Ser.No. 16/445,560, filed on Jun. 19, 2019, now U.S. Pat. No. 10,840,930,which is a continuation of U.S. patent application Ser. No. 15/986,084,filed on May 22, 2018, now U.S. Pat. No. 10,374,622, which is acontinuation of PCT Application No. PCT/CN2018/071475, filed on Jan. 5,2018, the entire disclosure of each of which is incorporated herein byreference.

BACKGROUND

The preferred embodiments relate to digital-to-analog converters andsystems including such convertors.

A digital-to-analog converter (“DAC”) is a device or configuration thatreceives a digital input and provides an output voltage proportional tothe value of the digital input. The digital value may follow standardbinary representation or Gray code values, in which each successivevalue is represented by only a single bit change versus the value thatprecedes it. There are various DAC architectures currently used in theart, and selection of a particular architecture may depend on theapplication and with a view to certain performance and design metrics,such as power consumption, speed, glitch magnitude and energy, the arearequired to implement the device, and so forth.

Thus, while prior approaches have been workable in some applications,the present inventor seeks to improve upon the prior art, as furtherdetailed below.

SUMMARY

In an embodiment, there is a digital-to-analog converter for generatingan analog output voltage in response to a digital value comprising aplurality of bits, the converter comprising: (i) a first switchedresistor network having a first configuration and for converting a firstinput differential signal into a first analog output in response to afirst set of bits in the plurality of bits; and (ii) a second switchedresistor network, coupled to the first switched resistor network, havinga second configuration, differing from the first configuration, and forconverting a second input differential signal into a second analogoutput in response to a second set of bits in the plurality of bits.

Numerous other inventive aspects are also disclosed and claimed.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

FIG. 1 illustrates an electrical and functional block diagram of adigital-to-analog converter (DAC) system according to a preferredembodiment.

FIG. 2 illustrates an electrical block and schematic diagram of the MSBstage of the system from FIG. 1 .

FIG. 3A illustrates an electrical block and schematic diagram of the ISBstage of the system from FIG. 1 .

FIG. 3B illustrates the ISB stage of FIG. 3A with switch positions inresponse to an ISB Gray code of 00000.

FIG. 3C illustrates the ISB stage of FIG. 3B with an equivalentresistance for the last sub-stage.

FIG. 3D illustrates the ISB stage of FIG. 3B with an equivalentresistance for the last two sub-stages.

FIG. 3E illustrates the ISB stage of FIG. 3B with an equivalentresistance for all sub-stages.

FIG. 4A illustrates an electrical block and schematic diagram of the LSBstage of the system from FIG. 1 .

FIG. 4B illustrates an equivalent resistance of the LSB stage of FIG. 4Awith switch positions in response to LSB sequence of 0000.

FIG. 4C illustrates an equivalent resistance of the LSB stage of FIG.4A.

FIG. 5 illustrates an electrical block and schematic diagram of analternative preferred embodiment of the LSB stage of the system fromFIG. 1 .

FIG. 6 illustrates the DAC system of FIG. 1 with an additional outputbuffer and an offset cancellation circuit incorporated into the LSBstage.

FIG. 7 illustrates a schematic representation of a first offsetcancellation circuit incorporated into the LSB stage.

FIG. 8 illustrates a schematic representation of a second, alternative,offset cancellation circuit incorporated into the LSB stage.

FIG. 9 illustrates a preferred embodiment offset cancellation circuitfor implementing offset cancellation using the Voc signal from FIG. 7 .

FIG. 10 illustrates a preferred embodiment offset cancellation circuitfor implementing offset cancellation using the differential Voc_H andVoc_L signals from FIG. 8 .

DETAILED DESCRIPTION

FIG. 1 illustrates an electrical and functional block diagram of adigital-to-analog converter (DAC) system 100, according to a preferredembodiment. By way of introduction, system 100 converts a digital binaryvalue dac_bin to a proportional analog output voltage Vdac_out, where inthe example of FIG. 1 (and later Figures) dac_bin has a total of 12bits—hence, shown by typical convention as dac_bin<11:0>. The use of 12bits is by way of example, as various inventive concepts may be appliedto other number of binary values. In that example, therefore, fordac_bin<11:0>=000000000000, an analog signal of Vdac_out will berelatively low (e.g., equal to or approaching a relatively low supplyvoltage, such as ground), while for dac_bin<11:0>=111111111111, ananalog signal of Vdac_out will be relatively high (e.g., equal to orapproaching a high supply voltage for system 200).

In a preferred embodiment, system 100 includes at least two stages, andpreferably in one preferred embodiment three different stages, eachresponsive to a subset of the digital binary value dac_bin. Asillustrated in FIG. 1 , a three stage preferred embodiment includes: (i)a most significant bits (MSB) stage 200; (ii) an intermediatesignificant bits (ISB) stage 300; and (iv) a least significant bits(LSB) stage 400. MSB stage 200 is biased between voltage rails VrefH andVrefL and receives the MSBs of dac_bin<11:0>, where in the exampleillustrated the number of MSBs equals three. In response to those (e.g.,three) MSBs dac_bin<11:9>, MSB stage 200 outputs different rail signalsV(Rtop) and V(Rbot) to ISB stage 300, where the magnitude of V(Rtop) andV(Rbot) is proportional to the digital value of dac_bin<11:9>. ISB stage300 is therefore biased between voltage rails V(Rtop) and V(Rbot) andreceives the ISBs of dac_bin<11:0>, where in the example illustrates thenumber of ISBs so received equals five. In response to those (e.g.,five) ISBs dac_bin<8:4>, ISB stage 300 outputs different rail signals VHand VL to LSB stage 400, where the magnitude of VH and VL isproportional to the digital value of dac_bin<8:4>, and furtherproportional therefore to the single MSB stage 200 preceding ISB stage300. LSB stage 400 is therefore biased between voltage rails VH and VLand receives the LSBs of dac_bin<11:0>, where in the example illustratesthe number of ISBs so received equals four. In response to those (e.g.,four) LSBs dac_bin<3:0>, LSB stage 400 outputs the system output voltageVdac_out, which will be proportional to the digital value ofdac_bin<3:0>, and further proportional therefore to the two stages,namely MSB stage 200 and ISB stage 300, preceding LSB stage 400. Each ofthe three stages is further detailed below.

FIG. 2 illustrates an electrical block and schematic diagram of MSBstage 200 in greater detail. Each of the voltage rails VrefH and VrefLis connected to a respective node 202 and 204, and a switchdecode/control block 205 receives the MSBs, namely, dac_bin<11:9>. Asfurther appreciated below, stage 200 includes a number of switches,where each switch is preferably implemented in a same form, such as viaone or more transistors, or the like. The opening and closing of eachswitch is in response to a control signal from switch decode/controlblock 205, as shown generally by way of dashed arrows. As furtherdetailed below, the selective closing of switches is preferably to closeonly one switch at a time in the set of eight switches connected to node202 and concurrently only one switch in the set of eight switchesconnected to node 204. As also appreciated below, stage 200 includes anumber of resistors, so the selective closing of switches effectivelychanges the overall realized (or realizable) equivalent resistance ofstage 200 as a whole, thereby changing the stage dividing effect asbetween the voltage rails VrefH and VrefL. To further appreciate theselectability or changing effective resistance of stage 200, note thatnodes 208 and 210 also are loaded by an equivalent resistance from theISB stage 300 and LSB stage 400 driven by those nodes, where as detailedbelow the resistance of that stage is twice a unit resistance, indicatedtherefore in FIG. 2 as a resistance of 2R.

In connection with node 202, a first terminal of seven evenly-numberedswitches 208SW1 through 220SW1 is connected to node 202, and a secondterminal of those seven switches is connected to a first terminal of arespective one of evenly-numbered resistors 204R1 through 216R1, wherethe second terminal of each of resistors 204R1 through 216R1 isconnected to a node 208. A first node of an eighth switch 222SW1 isconnected to node 202, and a second node of switch 222SW1 is connectedto node 208. Node 208 also provides the above-introduced rail voltage,V(Rtop). Note that resistance values of the resistors in stage 200 (andin later stages) are described relative to a unit resistance 1R, meaningeach resistor has an integer multiple resistance of a nominal unitvalue, where for example that nominal value can be 20 kΩ, in which casethe intent is that a resistor of resistance 1R has that same resistanceof 20 kΩ, a resistor of resistance 2R has twice that resistance, thatis, of 40 kΩ, and so forth. Note also that resistance value will dependon total resistance, drive current, and voltage reference, so by way ofexample a 1R unit resistance could be in the 1 kΩ to 40 kΩrange. Withthis explanation, in the illustrated preferred embodiment, the multipleunit resistance of each of the seven resistors having a terminalconnected to node 208 are as shown in the following Table 1:

TABLE 1 Resistor Unit resistance 204R1 14R  206R1 12R  208R1 10R  210R18R 212R1 6R 214R1 4R 216R1 2R

In connection with node 204, a first terminal of seven evenly-numberedswitches 210SW2 through 222SW2 is connected to node 204, and a secondterminal of those seven switches is connected to a first terminal of arespective one of evenly-numbered resistors 206R2 through 218R2, wherethe second terminal of each of resistors 206R2 through 218R2 isconnected to a node 210. A first node of an eighth switch 208SW2 isconnected to node 204, and a second node of switch 208SW2 is connectedto node 210. Node 210 also provides the above-introduced rail voltage,V(Rbot). Further, having introduced the unit resistance 1R, in theillustrated preferred embodiment, the multiple unit resistance of eachof the seven resistors having a terminal connected to node 210 are asshown in the following Table 2:

TABLE 2 Resistor Unit resistance 206R2 2R 208R2 4R 210R2 6R 212R2 8R214R2 10R  216R2 12R  218R2 14R 

The operation of MSB stage 200 is now described in greater detail. MSBsdac_bin<11:9> are input to block 205, and in response, either or both ofvoltages V(Rtop) and V(Rbot) are adjusted to provide a seconddifferential ΔV2, which is proportional to the value of the MSBs and afunction of the differential voltage ΔV1 between VrefH and VrefL. Asintroduced above, the three MSBs cause a simultaneous closing of onlyone switch in the set of switches connected to node 202 and one switchin the set of switches connected to node 204 and, thus, each resistor ina first set of resistors (204R1 through 216R1) is switchably selectableto connect between the node 202 and node 208, and each resistor in asecond set of resistors (206R2 through 218R2) is switchably selectableto connect between node 204 and node 210. Note now that the first threeintegers used in reference numbering those switches is intended toindicate that like numbered switches are closed at a same time—forexample, if the MSBs cause switch 208SW1 to close, then those same MSBscause switch 208SW2 to simultaneously close. Continuing with thatexample in which switch 208SW1 closes (at the same time as switch 208SW2closing), therefore, one skilled in the art will appreciate that VrefHis thereby connected through resistor 204R1, having a resistance of 14R,to node 208, thereby creating a series connection of the 14R fromresistor 204R1 to the ISB/LSB equivalent resistance of 2R, for a totalseries resistance of 16R, and as a result of voltage division, 7/8 ofVrefH is across the 14R resistance of resistor 204R1 (i.e.,14R/16R=7/8), while the remaining ⅛ of VrefH is across the 2R equivalentresistance of the ISB/LSB stages (i.e., 2R/16R=⅛) and is thereforeoutput as V(Rtop). Also with the example where switch 208SW2 closes (atthe same time as switch 208SW1 closing), VrefL is thereby connecteddirectly to node 210, in which case the voltage at node 210 equals VrefLwhich, as a lower rail voltage, may equal ground. Having provided oneexample of the concurrent like-numbered switches closing and theresultant voltages at V(Rtop) and V(Rbot), the following Table 3illustrates all possibilities of the three MSBs, and the correspondingswitch pair closed by decode/control by block 205 in response to thoseMSBs as well as the resultant voltages at V(Rtop) and V(Rbot), wherethose voltages are shown as VrefH, VrefL, or in proportion to thedifferential voltage of VrefH−VrefL=ΔV1:

TABLE 3 Switch pair dac_bin<11:9> closed V(Rtop) V(Rbot) 000 208[(1/8)*ΔV1] + VrefL VrefL 001 210 [(2/8)*ΔV1] + VrefL [(1/8)*ΔV1] +VrefL 010 212 [(3/8)*ΔV1] + VrefL [(2/8)*ΔV1] + VrefL 011 214[(4/8)*ΔV1] + VrefL [(3/8)*ΔV1] + VrefL 100 216 [(5/8)*ΔV1] + VrefL[(4/8)*ΔV1] + VrefL 101 218 [(6/8)*ΔV1] + VrefL [(5/8)*ΔV1] + VrefL 110220 [(7/8)*ΔV1] + VrefL [(6/8)*ΔV1]] + VrefL  111 222 [(8/8)*ΔV1] +VrefL [(7/8)*ΔV1] + VrefL

Given the preceding and the values in Table 3, it may be generallyobserved that at the MSB maximum (i.e., MSB=dac_bin<12:9>=111), V(Rtop)is the highest achievable output from the eight (i.e., 3²=8)combinations of MSBs, that is, V(Rtop) equals the full differential ofΔV1 (i.e., VrefH-VrefL)+VrefL, while V(Rbot) is [(⅞)*ΔV1]+VrefL, thatis, (⅛)*ΔV1 below V(top). Moreover, with each successive decrement ofthe MSBs (e.g., 111, 110, 101, . . . ), then each of nodes 208 and 210decreases by (⅛)*ΔV1. Thus, for a change in the MSBs, the differentialbetween V(Rtop) and V(Rbot) remains constant while each respective railV(Rtop) and V(Rbot) decreases by (⅛)*ΔV1 for each sequential decrement.Moreover, when the combined MSBs reach a minimum (i.e.,MSB=dac_bin<12:9>=000), V(Rbot) is the lowest achievable output from theeight combinations of MSBs, that is, V(Rbot) equals RrefL, and againV(Rtop) is ⅛*ΔV1 higher than V(Rbot). In all instances, the adjustablerail voltages, with a common voltage differential, are thereby presentedas ΔV2 to the next stage, that is, to ISB stage 300, as further exploredbelow.

FIG. 3 illustrates an electrical block and schematic diagram of ISBstage 300 in greater detail. By way of introduction, stage 300 includesan R-2R resistor ladder, which in some prior implementations is the soleapproach for converting a digital signal to an analog signal—in thisregard, the configuration is referred to as a ladder for includingmultiple sub-stages, whereby each sub-stage includes a first and secondresistance, where either the intermediate node between the two or theterminal end of the second resistance provides a switchable input to thenext sub-stage. Indeed, as described later, a preferred embodiment ofmultiple stages results in considerable improvement over such anapproach, particularly in a reduction in the resistance values neededfor the ADC conversion. Also by way of introduction, additionalinformation with respect to an ADC R-2R resistor ladder may be found inU.S. Pat. No. 4,591,826, issued May 27, 1986 to Seiler, which is fullyincorporated herein by reference.

ISB stage 300 receives the voltage V(Rtop) as connected to a node 302and the voltage V(Rbot) as connected to a node 304. A double pole,double throw (DPDT) switch 306 is connected from nodes 302, 304, toswitch between those nodes and a respective pair of nodes 308 and 310,where switch 306 is shown by dashed lines; hence, switch 306 in a firstposition connects node 302 to node 308, while concurrently connectingnode 304 to node 310, and switch 306 in a second position connects node302 to node 310, while concurrently connecting node 304 to node 308.Control of switch 306 to either of these positions is in response to aGray code bit B<4>. Further in this regard, system 300 includes abinary-to-Gray code converter 312 which receives the five ISBsdac_bin<8:4> and converts those to an equivalent five bit Gray codeB<4:0>, where Gray codes are known to provide an increasing sequence ofbits, where for each incremental value only a single bit changes in thecode as compared to the bit code that immediately preceded it. Furtherin this regard, each bit in the Gray code B<4:0> operates a respectiveswitch in stage 300 as further detailed below, so the nature of Graycodes permitting only one bit to switch state at a time willcorrespondingly cause only one switch in stage 300 to change state at atime, thereby improving performance (e.g., reducing switching-inducednode and power consumption). Accordingly, bit B<4> controls switch 306as described above, and further such that when B<4>=0, theabove-described first position is achieved, whereas when B<4>=1, theabove-described second position is achieved.

Continuing with the devices and connections in stage 300, node 308 alsoconnects to a first terminal of a resistor 314, with a unit resistanceof 1R and having a second terminal connected to a node 316. Node 316also connects to a first terminal of a resistor 318, with a unitresistance of 2R and having a second terminal connected to node 310. Therelationship of the 1R resistance of resistor 314 to the 2R resistanceof resistor 318 aligns with the reference to the configuration as anR-2R configuration. A DPDT switch 320, controlled by Gray code bit B<3>,is connected from nodes 316, 310, to switch between those nodes and arespective pair of nodes 322 and 324. Node 322 also connects to a firstterminal of a resistor 326, with a unit resistance of 1R and having asecond terminal connected to a node 328. Node 328 also connects to afirst terminal of a resistor 330, with a unit resistance of 2R andhaving a second terminal connected to node 324. A DPDT switch 332,controlled by Gray code bit B<2>, is connected from nodes 328, 324, toswitch between those nodes and a respective pair of nodes 334 and 336.Node 334 also connects to a first terminal of a resistor 338, with aunit resistance of 1R and having a second terminal connected to a node340. Node 340 also connects to a first terminal of a resistor 342, witha unit resistance of 2R and having a second terminal connected to node336. A DPDT switch 344, controlled by Gray code bit B<1>, is connectedfrom nodes 340, 336, to switch between those nodes and a respective pairof nodes 346 and 348. Node 346 also connects to a first terminal of aresistor 350, with a unit resistance of 1R and having a second terminalconnected to a node 352. Node 352 also connects to a first terminal of aresistor 354, with a unit resistance of 2R and having a second terminalconnected to node 348. A DPDT switch 344, controlled by Gray code bitB<0>, is connected from nodes 352, 348, to switch between those nodesand a respective pair of nodes 358 and 360. Node 358 also connects to afirst terminal of a resistor 362, with a unit resistance of 1R andhaving a second terminal connected to a node 364. Lastly, nodes 364 and360 provide respective rail voltages VH and VL to LSB stage 400 (seeFIGS. 1 and 4A), and as illustrated in FIG. 3 that stage provides anequivalent resistance load of 1R to MSB stage 300.

The operation of ISB stage 300 is now described in additional detail. Asintroduced above, as the ISBs (e.g., dac_bin<8:4>) are input to system100, they are converted by converter 312 to a Gray Code B<4:0>, withthat conversion shown in the first two columns of the following Table 4:

TABLE 4 dac_bin<8:4> B<4:0> VH VL 00000 00000  [(1/32)*ΔV2] + V(Rbot)V(Rbot) 00001 00001  [(1/32)*ΔV2] + V(Rbot)  [(2/32)*ΔV2] + V(Rbot)00010 00011  [(3/32)*ΔV2] + V(Rbot)  [(2/32)*ΔV2] + V(Rbot) 00011 00010 [(3/32)*ΔV2] + V(Rbot)  [(4/32)*ΔV2] + V(Rbot) 00100 00110 [(5/32)*ΔV2] + V(Rbot)  [(4/32)*ΔV2] + V(Rbot) 00101 00111 [(5/32)*ΔV2] + V(Rbot)  [(6/32)*ΔV2] + V(Rbot) 00110 00101 [(7/32)*ΔV2] + V(Rbot)  [(6/32)*ΔV2] + V(Rbot) 00111 00100 [(7/32)*ΔV2] + V(Rbot)  [(8/32)*ΔV2] + V(Rbot) . . . . . . . . . . . .. . . . . . . . . . . . 11100 10010 [(29/32)*ΔV2] + V(Rbot)[(28/32)*ΔV2] + V(Rbot) 11101 10011 [(29/32)*ΔV2] + V(Rbot)[(30/32)*ΔV2] + V(Rbot) 11110 10001 [(31/32)*ΔV2] + V(Rbot)[(30/32)*ΔV2] + V(Rbot) 11111 10000 [(31/32)*ΔV2] + V(Rbot)[(32/32)*ΔV2] + V(Rbot)The Table 4 left two columns thus illustrate the above-described natureof the Gray code, that is, as the five MSBs in the binary code dac_binincrement, a corresponding Gray code is provided and it only changes onebit at a time. For example, consider the increase of binary code dac_binfrom 00011 to 00100. In the binary sense, all three of the lowersignificant bits in that sequence change; however, the correspondingGray code conversion provides a sequence from 00010 to 00110, in whichcase only the third bit changes, namely, from 0 to 1. Moreover, fromFIG. 3 , that third bit is bit B<2>, so in this instance only switch 332changes position, while the other four switches do not. Further, theswitch change connects node 328 to node 336 and node 324 to node 334,thereby causing a change in the voltage division from stage 300, as willbe further appreciated below.

The voltage division achieved by the various resistors in stage 300 andthe selective change in node connectivity, by virtue of switches 306,320, 332, 344, and 356, is now further described. By way of example,consider the instance where dac_bin<8:4>=00000 and, as shown in Table 4,likewise the corresponding Gray code B<4:0> therefore also=00000. Inthis case, each switch in FIG. 3A connects along what are shown as thehorizontal dashed lines, thereby establishing a resistor ladder as shownin FIG. 3B, namely, with four sub-stages, meaning the combination of a1R resistor connected to a 2R resistor, where the intermediate nodebetween the resistors provides an output for a next sub-stage, and wherethe ladder essentially includes what can be characterized as a final,fifth sub-stage from the 1R resistance of resistor 362 and the 1Requivalent resistance from the LSB stage that is connected to nodes 364and 360. In this configuration, the 1R resistance of resistor 362 andthe 1R equivalent resistance of the LSB stage may be considered, from acircuit analysis standpoint an equivalent 2R total series resistanceReq1, which therefore is in parallel with the 2R resistance of resistor354, as shown in FIG. 3C. Continuing, therefore, the two same resistancevalues of 2R in parallel (i.e., of resistor 354 and equivalentresistance Req1) create an equivalent resistance Req2 of 1R betweennodes 352 and 348, as shown in FIG. 3D. Similar to the analysis of FIG.3A, therefore, again the far right end of the equivalent network has twoseries connected 1R resistances, here being resistor 350 and equivalentresistance Req2, connected in parallel with a 2R resistance, hereresistor 342. From these observations, one skilled in the art should beable to readily confirm that such impedance equivalence can continue foreach successive sub-stage, ultimately yielding the equivalent resistanceshown in FIG. 3E. Specifically, FIG. 3E illustrates a final equivalentresistance diagram in which between the input rail voltages areconnected a resistor 314 with a 1R resistance and a 1R equivalentresistance Req3, with one output node 316 between the two resistors andanother output node 304 at the end of the two-resistor connection,thereby creating a differential output voltage across the 1R equivalentresistance Req3. Further, because the resistance of resistor 314 andequivalent resistance Req3 are equal (e.g., 1R), then a ½ input voltagedivider is created, that is, the output voltage for this equivalentresistance is (½)*ΔV2.

Having demonstrated above that a singular sub-stage equivalentresistance of output=(½)*(input differential voltage), note that thesame principle applies equally across each sub-stage in FIG. 3B (i.e.,in response to dac_bin<8:4>=B<4:0>=00000). Thus, each stage, whenswitched to the configuration of 3B multiplies its input times ½, so thetotal of five stages produce a divider of

$\left( \frac{1}{2} \right)^{5} = {\frac{1}{32}.}$Returning to Table 4, note then that the first data row therein,corresponding to the case of dac_bin<8:4>=B<4:0>=00000, thusly providesan upper rail output VH of [( 1/32)*ΔV2]+V(Rbot); meanwhile, as readilyseen by the connections of any of FIG. 3A through FIG. 3E, the sameswitched configuration directly connects V(Rbot) to VL, as also shown inthe first data row of Table 4. Lastly, given the now-described exampleof the first row of Table 4 and FIGS. 3A through 3E, one skilled in theart may readily provide a comparable analysis for each other row byevaluating the realized equivalent resistance per sub-stage and theresultant voltage division achieved, thereby confirming the remainingindications in Table 4. In all instances, the adjustable rail voltagesof VH and VL will have a common voltage differential of ( 1/32)*ΔV2, butnote that the DPDT switches permit in certain instance either VH>VL orVL>VH, and in any event that difference is thereby presented as ΔV3 tothe next stage, that is, to LSB stage 400, as further explored below.

FIG. 4A illustrates an electrical block and schematic diagram of LSBstage 400 in greater detail. Each of the voltage rails VH and VL (fromthe output of ISB stage 300) is connected to a respective node 402 and404, and a switch decode/control block 406 receives the LSBs, namely,dac_bin<3:0>. Like block 205 in stage 200, block 406 converts bits, herefour LSB bits, into a control to selectively close one of sixteenevenly-numbered switches 408SW through 438SW at a time. Particularly,each of switches 408SW through 438SW has a first terminal connected toan output node 440 and a second terminal connected to a first terminalof a respective one of evenly-numbered 1R unit resistance resistors408RR through 438RR, where resistors 408RR through 438RR form aseries-string of resistors connected between node 402 and node 404. Thesecond terminal of each of resistors 410RR through 438RR is connected tothe first terminal of a respective resistor below it in the seriesconnection of resistors 408RR through 438RR, where, for example, thesecond terminal of resistor 438R is connected to the first terminal ofresistor 436RR, the second terminal of resistor 436R is connected to thefirst terminal of resistor 434RR, and so forth through, but the lastseries-connected resistor 408RR has its second terminal connected tonode 404. Resistor 438RR is also one of sixteen 1R unit resistanceresistors, all connected as part of a resistor set 442, each connectedin parallel, that is, between node 402 and a node 444. Lastly, anadditional resistor 446, having a single unit resistance 1R, isconnected between node 444 and node 404.

The operation of LSB stage 400 is now described in additional detail. Asintroduced above, as the LSBs (e.g., dac_bin<3:0>) are input to system100, they are converted to a control signal to close one of switches408SW through 438SW at a time, with the selected closed switch, and thecorresponding LSB bits that cause such closure, shown in the first twocolumns of the following Table 5:

TABLE 5 dac_bin<3:0> Switch closed Vdac_out 0000 408SW  [(1/16)*ΔV3] +VL 0001 410SW  [(2/16)*ΔV3] + VL 0010 412SW  [(3/16)*ΔV3] + VL 0011414SW  [(4/16)*ΔV3] + VL 0100 416SW  [(5/16)*ΔV3] + VL 0101 418SW [(6/16)*ΔV3] + VL 0110 420SW  [(7/16)*ΔV3] + VL 0111 422SW [(8/16)*ΔV3] + VL 1000 424SW  [(9/16)*ΔV3] + VL 1001 426SW[(10/16)*ΔV3] + VL 1010 428SW [(11/16)*ΔV3] + VL 1011 430SW[(12/16)*ΔV3] + VL 1100 432SW [(13/16)*ΔV3] + VL 1101 434SW[(14/16)*ΔV3] + VL 1110 436SW [(15/16)*ΔV3] + VL 1111 438SW[(16/16)*VΔ3] + VL

The Table 5 left two columns thus illustrate the change in the LSBs andthe corresponding single selected switch that closes in response, andthe third column indicates the resultant voltage division in response tothat closed switch. That voltage division, achieved by the variousresistors and switches in stage 400, is now further described. By way ofexample, consider the instance where dac_bin<0:0>=0000 and, as shown inTable 5, switch 408SW closes, so the effective resulting circuit may beas illustrated in FIG. 4B. Toward the top of the Figure, the equivalentresistance of the 16 parallel 1R unit resistance resistors in set 444 isshown, that is, R/16, connected between nodes 402 and 444. Beneath node444 is the same single 1R unit resistance of resistor 446, and inparallel therewith are the 14 series connected 1R units resistors 410RRthrough 436RR having therefore a total resistance of 14R, further inseries with the single 1R unit resistor 408RR. Lastly, note that outputnode 440, by virtue of the closed switch 408SW (see FIG. 4A) in thecurrent example, is between the 14R resistance of 1R unit resistors410RR through 436RR and the single 1R unit resistor 408RR.

FIG. 4C illustrates the equivalent resistance of FIG. 4B, taking intoaccount the connections between nodes 444 and 404. Specifically, betweenthose nodes as shown in FIG. 4B are a parallel connection of a 1Rresistance (from 446) with a series connection of a 15R resistance (from408RR through 436RR). The resultant equivalent resistance Req4 from thatparallel connection is as shown in the following Equation 1:

$\begin{matrix}{{{Req}4} = {\frac{R*15R}{R + {15R}} = {\frac{15R^{2}}{16R} = \frac{15R}{16}}}} & {{Equation}1}\end{matrix}$Accordingly, as shown in FIG. 4C, stage 400 reduces to an equivalentresistance of R/16 above node 444 and 15R/16 below node 444, that is, avoltage divider is created with [( 1/16)*(VH−VL)]+VL above node 444 and[( 15/16)*(VH−VL)]+VL below node 444. In addition, note that the lower[( 15/16)*(VH−VL)]+VL is further divisible by the 15 resistors, andcorresponding switches, below node 444 as shown in FIG. 4A. For example,therefore, if switch 408SW is closed, then the lower[(15/16)*(VH−VL)]+VL below node 444 is divided by the one out of fifteenresistors (i.e., resistor 408RR) connected by the closed switch tooutput node 444, providing a resultant output voltage as shown in thefollowing Equation 2:

$\begin{matrix}{{Vdac}_{out} = {{\left\lbrack {\frac{15\left( {{VH} - {VL}} \right)}{16}*\frac{1}{15}} \right\rbrack + {VL}} = {\left\lbrack \frac{{{VH} - {VL}} = {V\Delta 3}}{16} \right\rbrack + {VL}}}} & {{Equation}2}\end{matrix}$Hence, Equation 2 confirms the first data row entry in Table 15, thatis, where dac_bin<3:0>=0000, switch 408SW closes and the output is thedifferential input divided by 16, plus VL. Moreover, one skilled in theart should now appreciate that as the LSBs (i.e., dac_bin<3:0>)increment, a next upper switch in the set of 16 switches, each connectedto a respective series-connected resistor, closes, thereby connecting anadditional 1/15 resistance between node 404 and the output, therebyincreasing the output by an additional ( 1/16)*VΔ3, as shown in Table 5.

Also contemplated in connection with stage 400 of FIG. 4A are variousalternatives. For example, while FIG. 4A illustrates a 16-bit voltagedivider, other variations, such as powers of 2, may be implemented inalternative preferred embodiments. In the illustrated or suchalternative instances, for an N-bit divider following the same generalschematic as in FIG. 4A, the number of parallel resistors in set 444 isN, the number of switches is N, and the number series resistors betweennodes 444 and 404 is N−1. In this manner, for example, an N=8 bitdivider may be constructed, with 8 parallel resistors between nodes 402and 444, 7 series resistors between nodes 444 and 404, and 8 switches,each connected from a respective first terminal of a resistor to anoutput node 440. As still another variation, note from Table 5 that thelowest voltage achievable is higher than VL (e.g., ( 1/16)*VΔ3), as theconfiguration does not facilitate a connection directly from node 404 tonode 440, so the lowest achievable output is the voltage across thebottom resistor 408RR (i.e., via switch 408SW) in the output resistorseries string. Hence, in an alternative preferred embodiment, a switchmay be added from node 404 to node 440, with the switch from node 402 tonode 440 removed; in this configuration, the lowest achievable outputwill be VL, although as a tradeoff the highest achievable output will nolonger by VH, in that no direct connection from node 402 to node 440 isthus achievable, so the highest such output voltage will be (15/16)*VΔ3, that is, the voltage across the N−1 resistors between node444 and node 404.

FIG. 5 illustrates an electrical block and schematic diagram ofalternative preferred embodiment LSB stage 500 in greater detail, as maybe substituted for LSB stage 400 of FIG. 4A. Specifically, it isrecognized and contemplated that in stage 400 of FIG. 4A, one terminalof each of the 16 switches connects directly to output node 440. As aresult, parasitic capacitance from such switches may cause speedlimitations of a signal swing on that node as well as potential glitchesin the output signal. Thus, LSB stage 500 provides an alternative inwhich such considerations may be improved, particularly for instanceswhere the number of LSBs is beyond a design threshold (e.g., greaterthan four LSBs).

The LSBs of stage 500, namely, dac_bin<3:0>, are splits into two sets,one being the lesser significant of those bits and the other being themore significant of those bits. The lesser significant of the LSBs,namely, dac_bin<1:0>, are connected to what will be referred to hereinas a serpentine decoder 502 which, as detailed later, is so named inthat those bits are decoded to a pattern that in response to successiveincrements in dac_bin<1:0>, and further in response to dac_bin<2>, theoutput of decoder 502 is such that, instead of wrapping around from itsmaximum of 3 back to 0 as would a typical 2-bit binary decoder, itinstead traces upward to its maximum, repeats that maximum and thendecrements back to its minimum, repeats that, and returns again in theopposite direction (e.g., 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, . . . ), forreasons of addressing a serpentine array pattern as more apparent later.Further in this regard, therefore, for each 2—bit input to decoder 502,the 1 of 4 output of serpentine decoder 502 thereby selects acorresponding column C0 through C3. The more significant of the LSBs,namely, dac_bin<3:2>, are connected to a binary decoder 504, whichoperates in standard binary conversion so that in response to successiveincrements in dac_bin<3:2>, the output of binary encoder 504 merelyincrements upward to its maximum and then repeats from its minimum(e.g., 0, 1, 2, 3, 3, 0, 1, 2, 3, . . . ), also for reasons moreapparent later. Further in this regard, therefore, for each 2-bit input,the 1 of 4 output of binary decoder 504 thereby selects a correspondingrow R0 through R3.

Each of the voltage rails VH and VL (from the output of ISB stage 300)is connected to a respective node 506 and 508. Between nodes 508 and 506is a series resistance string consisting of sixteen resistors evenlynumbered 510RR through 540RR. A first terminal of each of resistors510RR through 540RR, closer to node 506, is connected to a drain of arespective evenly numbered switching transistor 510T through 540T, and asource of each of switching transistor 510T through 540T is connected toone of four of columns C0 through C3, as shown in the following Table 6:

TABLE 5 Column Transistor source connected C0 510T, 524T, 526T, 540T C1512T, 522T, 528T, 538T C2 514T, 520T, 530T, 536T C3 516T, 518T, 532T,534TMoreover, each of switching transistors 510T through 540T has its gateconnected to one of four of row R0 through R3, as shown in the followingTable 6:

TABLE 6 Row Transistor source connected R0 510T, 512T, 514T, 516T R1518T, 520T, 522T, 524T R2 526T, 528T, 530T, 532T R3 534T, 536T, 538T,540TFrom Tables 5 and 6, also from FIG. 5 , note therefore that the seriesresistor string of resistors 510RR through 540RR, and the respectivetransistor connected to each resistor, is connected in a serpentinefashion, that is, upon traversing along a row of resistors, for examplefrom left to right, all coupled to respective transistors having gatescontrolled by a single row line, at the last column providing an end ofone row, rather than wrapping around to the first column (e.g., left) ofthe next row, the pattern is serpentine so as to end at the column oneof a row and then begin the next row at that same column. For example,consider the top row R3 of transistor 540T through 534T and theirrespective resistors 540TT through 534RR, moving from left (i.e., fromnode 506 and column C0) to right. At the right end of that row R3 areresistor 534RR and its respective transistor 534T coupled to column C3,but continuing in the series path of resistors, the next resistor 532RRin series is not at the left (i.e., column C0) end of the next row R2,but instead is at the right end of that next row R2 and the transistor532T connected to that next resistor 532RR is again connected toselectively output to column C3, that is, the same column to which thepreceding resistor 534RR may be connected. Indeed, continuing then fromcolumn C3 to the right and hen left along row R2, this same serpentinepattern repeats at the left end of row R2, which ends with resistor526RR being switchably connected to column C0 through respectivetransistor 526T, after which in series is resistor 524RR which is in thenext row R1, but at the left end and with a respective transistor 524TTfor switchably connecting resistor 524RR to the same column C0, and soforth also for the far right end of row R1. Given these connections, thedecoding table of serpentine decoder 502 is constructed to match theserpentine connectivity, so that an increase in the binary sequence ofbits dac_bin<1:0> is properly mapped from a column at one end of a rowto the same column for the next successive row; moreover, to accomplishsuch an operation, note further that in addition the two LSBsdac_bin<1:0> connected to decoder 502, so also is the next moresignificant bit dac_bin<2>, so as to enable the decoding shown in thefollowing Table 7:

TABLE 7 LSBs bit dac_bin<2> dac_bin<1:0> Column enabled 0 00 C0 0 01 C10 10 C2 0 11 C3 1 00 C3 1 01 C2 1 10 C1 1 11 C0Table 7 thus illustrates the enabled column follows the serpentinenature of the resistor string, for example as the LSBs dac_bin<2:0>increase from 000 to 111, with the serpentine effect occurring in thetransition of dac_bin<2:0>=011 to dac_bin<2:0>=100, as both cases resultin a selection of column C3. Moreover, note that Table 7 also applieswhen dac_bin<3> also transitions; for example, in the transition ofdac_bin<3:0>=0111 to dac_bin<3:0>=1000, note that per Table 7 both bitsets of bits causes column C0 to be enabled, again preserving theserpentine nature of column addressing so as to match the serpentineconstruction of the row/column/resistor/transistor layout of stage 500.Indeed, it is contemplated in connection with a preferred embodimentthat by accessing a same column twice during a ramping up or down ofdac_bin in this manner that a lower glitch rate and/or magnitude will beachieved as opposed to other approaches.

Also contemplated in connection with stage 500 of FIG. 5 are variousalternatives. For example, while FIG. 5 illustrates a 16-bit voltagedivider, other variations, such as powers of 2, may be implemented inalternative preferred embodiments. Indeed, for N>16, such an approachmay be favorable over stage 400 of FIG. 4A, as the latter will increasecapacitance by increasing N therein. To achieve more bits with stage500, than if N has an integer square root, then such an approach, likethat in FIG. 5 , will preferably implemented with √{square root over(N)} rows and √{square root over (N)} columns; however, if N does nothave an integer square root, then such an approach still may implementthe serpentine nature of the resistor divider illustrated in FIG. 5 ,but with a number of rows differing from the number of columns.

FIG. 6 again illustrates DAC system 100 of FIG. 1 , and adds to itadditional aspects. In FIG. 6 , the system 100 analog output of Vdac_outis coupled to a buffer 600, which may be constructed as an amplifier ina negative feedback configuration. In this regard, the output of buffer600 provides a corresponding analog signal output, Vdac_out_buff, andthe signal output is fed back to the inverting input of buffer 600,while Vdac_out is connected to the non-inverting input of buffer 600.

In another preferred aspect, note that buffer 600 may experience somelevel of DC offset, as is known in certain technologies. In the presentcontext, note further that the offset may exceed the resolution obtainedby the three stages of system 100. For example, consider the instancewhere VrefH=3.0V and VrefL is ground, and recall that stages 200, 300,and 400 together provide a 16 bit DAC. Thus, the DAC provides 2¹⁶=4,096different voltage divisions of the differential voltage input 3.0V, sothe resolution obtainable is 3.0V/4096=0.732 millivolts. However, adevice such as buffer 600 may have a DC offset in the range of ±3millivolts, for a total swing of 6 millivolts. In other words, the DCoffset is approximately 8 times larger than the resolution obtainable bystages 200, 300, and 400, so that obtainable resolution can be overlaidwith considerable error introduced by the 6 millivolt swing in thebuffer DC offset. Further in this regard, therefore, one preferredembodiment further augments LSB stage 400, or a portion thereof, so thatLSB stage 400 provides both the already-described output Vdac_out, butin addition provides a voltage offset cancellation signal, Voc, coupledto an offset control input of buffer 600 so as to correct (i.e., adjustso as to reduce) the DC offset within the achievable resolution for theDAC, as further described below. Further in this regard, FIG. 6 alsoillustrates an offset cancellation control signal OCCS is shown, withfour bits (i.e., OCCS<3:0>), as an input to LSB stage 400 and so as tofacilitate the offset cancellation. The OCCS bits may come from aseparate circuit, such as the processor or controller of which DAC 100serves or is a part of, and where that signal may be established duringmanufacture, start-up or the like, and then stored in memory for laterDC offsetting of buffer 600.

FIG. 7 illustrates a schematic representation of offset cancellationcircuit 602, which as introduced above with respect to FIG. 6 is, in apreferred embodiment, incorporated into LSB stage 400. Continuing withthe example of the preceding paragraph, in which the buffer DC offset isapproximately 8 times the resolution achievable by the ADC, then thesame swing of 8 times that resolution can be achieved from using thevoltage across 8 of the series-string resistors therein because thevoltage across any one of those resistors represents the lowestresolution of the DAC, so across 8 of those resistors is approximatelythe same voltage as the DC offset swing of buffer 600. Moreover,according to a preferred embodiment, the voltage across each of thoseresistors is preferably further subdivided into a number of equal stepsso as to provide additional resolution or granularity for tuning theoffset of buffer 600 by way of Voc. In the example of FIG. 7 ,therefore, such additional resolution is four parts per series-stringresistor, that is, circuit 602 provides a so-called ¼ step divider,meaning that the circuit is configured and operable to divide itsdifferential rail voltage into ¼ steps (e.g., 0, ¼, 2/4, ¾), as furtherunderstood below.

Looking in more detail at the FIG. 7 , offset cancellation circuit 602preferably replaces the lowest resistor 408RR in stage 400 with a ¼ stepcircuit output for use as a voltage offset cancellation Voc from a node604, while still also providing a switchable voltage from an output node408RUN to node 440. By replacing only a single resistor (e.g., resistor408RR) with a ¼ step circuit, such an implementation provide only the ¼step for the voltage swing across resistor 408RR (i.e., (VH−VL)/4096).Thus, if additional voltage swing selection is desired for offsetcancellation, a number of additional resistors in the series stringcontaining resistors 408RR through 438RR may be likewise replaced with acircuit of the configuration of circuit 602.

Looking then at circuit 602 in more detail, the circuit is shown betweennodes 408RUN and 404, which note in the condensed illustration of FIG. 7of stage 400 are the nodes at the upper and lower terminals,respectively, of resistor 408RR. Moreover, the offset cancellationcontrol signal OCCS from FIG. 6 is shown in more detail, with four bits(i.e., OCCS<3:0>), with each of the four bits to control a respectiveone of four switches 606, 608, 610, and 612 in circuit 602. Each bit inOCCS<3:0>, if enabled, selectively closes a respective one of the fourswitches 606, 608, 610, and 612 at a time, so as to provide a selectedvoltage to an output node 604 from the other terminal of the closedswitch, and thereby providing the offset voltage Voc to buffer 600.Particularly, each of switches 604, 606, and 608 has a first terminalconnected to output node 604 and a second terminal connected to a firstterminal of a respective one of evenly-numbered 1R unit resistanceresistors 614 through 618; in addition, switch 612 has a first terminalconnected to output node 604 and a second terminal connected to a node620, where there are four unit 1R resistors 622, 624, 626, and 628connected in parallel between that node 620 and node 408RUN. Lastly, anadditional resistor 630, having a single unit resistance 1R, isconnected between node 620 and node 404.

Given the preceding, the reader should comprehend various similaritiesof the structure of circuit 602 to others set forth above and theequivalent resistances achievable by selecting closure of any one ofswitches 606, 608, 610, and 612. In general, therefore: (i) the fourparallel resistors 622, 624, 626, and 628 provide an equivalentresistance of (R/4); and (ii) the parallel connection of resistor 630 tothe series connected resistors 614, 616, and 618 provide an equivalentresistance of (3R/4)—thus, items (i) and (ii) contribute in series todivide ¾ of the voltage between nodes 408RUN evenly between nodes 620and 404, so that: (A) node 404 voltage is selectable by switch 606; (B)¼ of the voltage between nodes 404 and 408RUN is selectable by switch608; (C) 2/4 of the voltage between nodes 404 and 408RUN is selectableby switch 610; and (D) ¾ of the voltage between nodes 404 and 408RUN isselectable by switch 612. Moreover, as introduced above, OCCS<3:0> maybe determined earlier and stored to select one of such switches, againproviding a resolution of (¼)*( 1/4096)*(VH−VL) and thus also theswitchable selection for Voc as any one of VL, (¼)*( 1/4096)*(VH−VL), (2/4)*( 1/4096)*(VH−VL), or (¾)*( 1/4096)*(VH−VL). Moreover, one skilledin the art also should now appreciate that, as introduced above, otherresistors in the series-string of stage 400 may likewise be replacedwith a comparable structure to circuit 602, in which additionalincrements of this resolution (e.g., (4/4)*( 1/4096)*(VH−VL), (5/4)*(1/4096)*(VH−VL), and so forth) may be provided. In addition, while theabove example illustrates a ¼ step, various design considerations or thelike may give rise to a different step size, in which case circuit 602is readily modified given the teachings of this document to provide moreor less resistors in the series string and in the parallel combinationconnected to the top node (or, could be bottom node), so as to achievethe different desired step size.

FIG. 8 illustrates a schematic representation of an alternativepreferred embodiment offset cancellation circuit 802, which, asintroduced above with respect to FIG. 6 and similar to circuit 602 ofFIG. 7 , is alternatively incorporated into LSB stage 400. Specifically,as known in the art, some buffer/amplifier circuits permit a DC offsetadjustment by way of a differential input and interpolation betweenthose inputs, for example by including a number (e.g., 16) ofdifferential transistor pairs responsive to the differential input. Anexample of such an approach may be found in U.S. Pat. No. 6,707,404,issued on Mar. 16, 2004, to Yilmaz, and co-owned by the assignee of thepresent patent application, and hereby incorporated herein by reference.In this regard, therefore, circuit 802 of FIG. 8 provides a modificationto circuit 602 of FIG. 7 , where the modification provides adifferential output voltage signal pair including Voc_H and Voc_L, wherethat pair is connected to buffer 600 for DC offset cancellation frominterpolation that may be incorporated into buffer 600 per the above.

Looking in more detail to circuit 802, it includes the same connectionsand generally the same designations as circuit 602, with the distinctionthat the letter “L” is added to one set of switches so as to designateswitches 606L, 608L, 610L, and 612L, all having a first terminalconnected to a node 604L, where all of these items are shown in FIG. 7as are the same connections, but without the “L” designation. Thus, inFIG. 7 , these items provide the singular output Voc, whereas in FIG. 8they provide one of the two differential signals, namely, Voc_L. Inaddition, however, an additional four switches 606H, 608H, 610H, and612H, are also included, each with a first terminal connected to a firstnode 604H that provides the second one of the two differential signals,namely, Voc_H; further, the second terminal of each of these fourswitches 606H, 608H, 610H, and 612H is connected to a respective higherpotential across each respective resistor, that is: (i) the secondterminal of switch 606H is connected to a terminal of resistor 614 thatis opposite the resistor 614 terminal that is connected to switch 606L;(ii) the second terminal of switch 608H is connected to a terminal ofresistor 616 that is opposite the resistor 616 terminal that isconnected to switch 608L; (iii) the second terminal of switch 610H isconnected to a terminal of resistor 618 that is opposite the resistor618 terminal that is connected to switch 610L; and (iv) the secondterminal of switch 612H is connected to a terminal of the parallelresistance of resistors evenly-numbered 622 through 628 that is oppositethe terminal of that parallel resistance that is connected to switch612L.

Given the preceding, the operation of circuit 802 should be readilyascertainable from the illustrations and descriptions of FIGS. 6 and 7 ,as well as the comparable teachings of earlier preferred embodiments.For circuit 802, when OCCS<3:0> specifies one of four switches, theintended illustration in FIG. 8 is that two switches close, each withthe same first three digit reference number. For example, ifOCCS<3:0>=0000, then switch 606L and 606H both close, with switch 606Lthereby connecting node 404 to node 606L and providing a first voltageas Voc_L and switch 606H thereby connecting the potential betweenresistors 614 and 616 to node 604H and providing a second voltage asVoc_H, with those two output voltages providing a differential DC offsetcorrection input to buffer 600. Moreover, the resistor dividingteachings of this document will therefore readily facilitate anunderstanding to one skilled in the art of the various voltage divisionsthereby switchably selectable for outputting, in the context of DCoffset correction.

FIG. 9 illustrates a preferred embodiment offset cancellation circuit902 for implementing offset cancellation in buffer 600 using the Vocsignal from FIG. 7 . Circuit 902 includes a first differential PMOStransistor pair including PMOS transistor 904 and PMOS transistor 906,each having a source connected to an output of a first current source908 that receives a power supply voltage (e.g., the supply to the entireDAC 100) VPS. The gate of PMOS transistor 904 receives the Vdac_outsignal from FIG. 7 (i.e., from node 440). The drain of PMOS transistor904 is connected to a node 910, and the drain of PMOS transistor 906 isconnected to a node 912. Node 910 is also connected to a non-invertinginput of an amplifier 914 and to a drain of an NMOS transistor 916,which has its source connected to ground. Node 912 is also connected toan inverting input of amplifier 914 and to a drain of an NMOS transistor918, which has its source connected to ground, and node 912 is alsoconnected to the gates of both of NMOS transistors 916 and 918. Circuit902 also includes a second differential PMOS transistor pair including aPMOS transistor 920 and a PMOS transistor 922, each having a sourceconnected a current source 924 that is connected to receive the voltageVPS. The drain of PMOS transistor 920 is connected to node 912 and thedrain of PMOS transistor 922 is connected to node 910. The gate of PMOStransistor 920 is connected to receive the Voc signal from FIG. 7 , andthe gate of PMOS transistor 922 is connected to node 404 from FIG. 7 ,which recall is also connected to the lower rail voltage VL.

The operation of circuit 902 is now described. First, note that theoutput signal Vdac_out_buff of amplifier 914 represents thebuffered/amplified/converted output from the three stages of system 100,with the further offset cancellation provided by circuit 902. Thus,Vdac_out_buff includes any offset voltage that is introduced by thebuffer/amplifier, but is also reduced (preferably toward zero) by anoffset cancellation voltage controlled by Voc. Further in this regard,therefore, note that the difference between Voc and VL, as applied tothe gates of PMOS pair 920 and 922, provides a first differential signalor current to nodes 910 and 912, and then the feedback connection fromthe output of amplifier 914, as provided to the gate of PMOS transistor906, and as a differential from Vdac_out applied to the gate of PMOStransistor 904, further adjusts the differential signals on nodes 910and 912. Hence, the feedback operates toward offsetting the DC offset ofthe amplifier, as stated above.

FIG. 10 illustrates a preferred embodiment offset cancellation circuit1002 for implementing offset cancellation in buffer 600 using thedifferential Voc_H and Voc_L signals from FIG. 8 . Various of thecomponents and connections in circuit 1002 are the same as circuit 902in FIG. 9 , so the reader is assumed familiar with those aspects. Inaddition, circuit 1002 includes a switch matrix 1004, which receives anumber B of interpolation offset cancellation bits IOCB, where in theexample illustrated B=4 and such bits are accordingly shown asIOCB<3:0>. Also input to switch matrix 1004 are the differential Voc_Hand Voc_L signals from offset cancellation circuit 802 of FIG. 8 .Switch matrix 1004 is connected to output these signals to therespective gates of 2^(B) PMOS transistor pairs, so for the exampleillustrated there are a total of 2^(B)=2⁴=16 PMOS transistor pairs TP1,. . . , TP15, TP16, where such pairs include the PMOS pair 920 and 922indicated as pair TP16. Each of these PMOS transistor pairs isconfigured in a manner comparable to PMOS pair 920 and 922, that is,with sources of the pair connected to a respective current source, adrain of the pair transistor that is connected to switchably receiveVoc_H at its gate connected to node 912, and a drain of the pairtransistor that is connected to switchably receive Voc_L at its gateconnected to node 910.

The operation of circuit 1002 is comparable to that of circuit 902, withthe additional operability to linearly interpolate between Voc_H andVoc_L in response to the IOCB<3:0> bits, which select a number oftransistor pairs to provide voltage to nodes 910 and 912. Specifically,the number of PMOS transistor pairs having an input connected to Voc_Hat a time is equal to the decimal value of the IOCB<3:0> bits that areapplied to switch matrix 1004. For example, if the IOCB<3:0> bits areequal to zero, all of the (+) inputs of PMOS transistor pairs TP1through TP16 are connected to Voc_L, and the output Vdac_out_buff ofamplifier 914 will then be equal to Voc_L. If the digital inputIOCB<3:0> bits are equal to 0001, then the (+) input of one of the PMOStransistor pairs TP1 through TP16 is connected to Voc_H, while the other(+) inputs are connected to Voc_L. Since one of 16 of the (+) inputs isconnected to Voc_H, that PMOS transistor pair adds an offsetcancellation voltage of (1)(Voc_H−Voc_L)/16 to amplifier 914. Similarly,with each increase of the digital input IOCB<3:0> bits, there is anincrease in the numerator multiplier for the generated offset voltageso, for example, if IOCB<3:0>=0010 (i.e., decimal value of 2), thenVoc_H is connected to the (+) gate input of a corresponding two pairs ofPMOS transistors, in which case collectively those two pairs add anoffset cancellation voltage of (2)(Voc_H−Voc_L)/16 to buffer 914. Aanother example, if IOCB<3:0>=0011 (i.e., decimal value of 3), thenVoc_H is connected to the (+) gate input of a corresponding three pairsof PMOS transistors, in which case collectively those three pairs add anoffset cancellation voltage of (3)(Voc_H−Voc_L)/16 to buffer 914. Hence,in general, the amount of offset voltage may be represented as in thefollowing Equation 3:

$\begin{matrix}{{{offset}{cancellation}{voltage}} = \frac{{decimal}{{value}\left( {{IOCB}\left\langle {3:0} \right\rangle} \right)}*\left( {{Voc\_ H} - {VocL}} \right)}{16}} & {{Equation}3}\end{matrix}$Accordingly, circuit 1002 provides an additional level of interpolationfor purposes of offsetting DC offset of buffer 914.

From the above, various preferred embodiments provide circuits and asystem that includes a digital to analog conversion with two or morestages having varying resistor/switching configurations. Further, thepreferred embodiments have been shown to have numerous benefits, andvarious embodiments have been provided. For example, preferredembodiments may be implemented based, for example, on unit resistancewith resistance values considerably lower than traditional ladder onlynetworks. Further, preferred embodiments may produce improvedperformance in terms of speed and reduced output glitches. As stillanother benefit, various modifications have been described and othersmay be contemplated or discernable by one skilled in the art, such asdiffering partitions the numbers of digital bits in a total digitalnumber to different stages of the converter, and differing step sizes ofresistor configurations described herein. Accordingly, while variousalternatives have been provided according to the disclosed embodiments,still others are contemplated and yet others may be ascertained. Giventhe preceding, therefore, one skilled in the art should furtherappreciate that while some embodiments have been described in detail,various substitutions, modifications or alterations can be made to thedescriptions set forth above without departing from the inventive scope,as is defined by the following claims.

The invention claimed is:
 1. A circuit comprising: a circuit stagecomprising: a first voltage input; a second voltage input; a set ofresistors coupled in series between the first voltage input and thesecond voltage input; a voltage output; and a voltage offset output; anda buffer comprising: a first input coupled to the voltage output of thecircuit stage; a second input coupled to the voltage offset output ofthe circuit stage; and a third input coupled to an output of the buffer.2. The circuit of claim 1, wherein the circuit stage further comprises aset of switches coupled between the set of resistors and the voltageoutput.
 3. The circuit of claim 1, wherein the set of resistors is afirst set of resistors, and the circuit stage further comprises a secondset of resistors coupled in parallel with the first set of resistors. 4.The circuit of claim 1, wherein the circuit stage comprises an offsetcircuit.
 5. The circuit of claim 4, wherein the offset circuitcomprises: a node coupled to the voltage offset output; a set ofswitches coupled to the node; and a first set of resistors coupledtogether in series and coupled to the set of switches.
 6. The circuit ofclaim 5, wherein the offset circuit further comprises: a second set ofresistors coupled together in parallel and coupled to a switch of theset of switches.
 7. A circuit device comprising: a first set of inputsconfigured to receive a reference voltage; a second set of inputsconfigured to receive a digital value; an output configured to providean analog voltage in response to the reference voltage and the digitalvalue; a set of stages coupled in series between the first set of inputsand the output, wherein the set of stages includes a first stage thatincludes: a first voltage input; a second voltage input; a set ofresistors coupled in series between the first voltage input and thesecond voltage input; a voltage output; and a voltage offset output; anda buffer comprising: a first input coupled to the voltage output of thefirst stage; a second input coupled to the voltage offset output of thefirst stage; and a third input coupled to an output of the buffer. 8.The circuit device of claim 7, the first stage further comprises a setof switches coupled between the set of resistors and the voltage output.9. The circuit device of claim 7, wherein the set of resistors is afirst set of resistors, and the first stage further comprises a secondset of resistors coupled in parallel with the first set of resistors.10. The circuit device of claim 7, wherein the first stage furthercomprises an offset circuit.
 11. The circuit device of claim 10, whereinthe offset circuit comprises: a node coupled to the voltage offsetoutput; a set of switches coupled to the node; and a first set ofresistors coupled together in series and coupled to the set of switches.12. The circuit device of claim 11, the offset circuit furthercomprises: a second set of resistor coupled together in parallel andcoupled to a switch of the set of switches.
 13. The circuit device ofclaim 7, wherein the voltage offset output is a first voltage offsetoutput, and the first stage further comprises a second voltage offsetoutput coupled to the buffer and an offset circuit, the offset circuitcomprising: a first set of switches coupled to the first voltage offsetoutput; and a second set of switches coupled to the second voltageoffset output.
 14. The circuit device of claim 13, wherein the offsetcircuit comprises a first set of resistors coupled together in seriesand coupled to the first set of switches and to the second set ofswitches.
 15. The circuit device of claim 14, wherein the offset circuitfurther comprises a second set of resistors coupled together in paralleland coupled to a first switch of the first set of switches and to asecond switch of the second set of switches.
 16. The circuit device ofclaim 7, wherein the first stage comprises an offset control signalinput.
 17. The circuit device of claim 7, wherein the buffer furthercomprises: a first transistor coupled to the voltage output of the firststage; a second transistor coupled to the voltage offset output of thefirst stage; and a third transistor coupled to the output of the buffer.18. The circuit device of claim 7, wherein the voltage offset output isa first voltage offset output and the first stage further a secondvoltage offset output, and the buffer further comprises a switch matrixcoupled to the first voltage offset output and the second voltage offsetoutput.
 19. The circuit device of claim 7, wherein the set of stagesincludes a second stage that includes: a first input; a second input; afirst output coupled to the first voltage input of the first stage; asecond output coupled to the second voltage input of the first stage;and a resistor ladder circuit.
 20. The circuit device of claim 19,wherein: the resistor ladder circuit includes a set of sub-stages; andeach sub-stage of the set of sub-stages includes: a first resistorcoupled between a respective first node and a respective second node; asecond resistor coupled between the respective second node and arespective third node; and a switch coupled to selectably couple: in afirst switch position, the respective first node of the sub-stage to therespective second node of a preceding sub-stage and the respective thirdnode of the sub-stage to the respective third node of the precedingsub-stage; and in a second switch position, the respective first node ofthe sub-stage to the respective third node of the preceding sub-stageand the respective third node of the sub-stage to the respective secondnode of the preceding sub-stage.